Generate curve from equation
The Add 3D Function Surface addon allows you to do exactly this. You can download this addon here. It also comes included in the built-in Extra Objects addon.

Once you have the addon installed, when you go to add a new mesh, you will have two additional options: 'Z function surface' and 'XYZ function surface'. If you select either of these, you will then be able to add parametric equations in the Toolbar menu to define your shape.

Example XYZ Function Surface: